帮我写一段用基础函数实现的可以成功运行的NTRU数字签名的MATLAB实验代码

好的，以下为实现NTRU数字签名的MATLAB代码，包括生成公钥、私钥以及签名、验证的部分：

% Step 1: Generate key pair

N = 503; % Polynomial degree
p = 3;
q = 128;
d = 68; % Private key degree

% Generate random f and g polynomials
f = zeros(N+1,1);
g = zeros(N+1,1);
f(1) = 1;
while sum(f) == 1 % Ensure f is not invertible modulo q
f = randi([-1,1],N+1,1).*mod(randi([0,q-1],N+1,1),q);
end
while sum(g) == 0 % Ensure g is invertible modulo p
g = randi([-1,1],N+1,1).*mod(randi([0,p-1],N+1,1),p);
end

% Calculate public key h
h = mod(conv(f,g),q);

% Calculate private key f_inv
f_poly = sparse(diag(f));
f_inv_poly = inv(f_poly);
f_inv_mod = mod(full(f_inv_poly),q); % Convert to mod q
f_inv = mod(f_inv_mod*f,q);

% Step 2: Signature generation

msg = 'Hello world!'; % Message to sign
h_poly = sparse(diag(h));
msg_poly = mod(int64(str2double(sprintf('%d ',msg))),q);
r_poly = randi([0,1],d,1).*mod(randi([0,q-1],d,1),q); % Random polynomial r
e_poly = mod(h_poly*r_poly + msg_poly,q); % Error polynomial e
s_poly = mod(f_poly*r_poly - f_inv_poly*e_poly,q); % Signature polynomial s

% Step 3: Signature verification

e_new_poly = mod(h_poly*s_poly - f_poly*msg_poly,q); % Calculate new error polynomial
if e_new_poly == e_poly % Verify signature
disp('Signature valid!');
else
disp('Signature invalid!');
end